設(shè)長(zhǎng)方體的3個(gè)棱長(zhǎng)分別為2x,2y,2z,
則x,y,z>0, x^2+y^2+z^2=A^2.
長(zhǎng)方體的體積f(x,y,z)=(2x)(2y)(2z)=8xyz.
設(shè)F(x,y,z)=8xyz+a(x^2+y^2+z^2-A^2),
令
DF/Dx【F對(duì)x的偏導(dǎo)數(shù)】 = 8yz + 2ax = 0,
DF/Dy = 8xz + 2ay = 0,
DF/Dz = 8xy + 2az = 0,
x^2 + y^2 + z^2 - A^2 = 0.
8yz*8xz*8xy=-(2ax)(2ay)(2az),
64(xyz)=-a^3,
xyz=-a^3/64,a